INTEGRABILITY OF VECTOR FIELDS AND MEROMORPHIC SOLUTIONS

• Tipo: Artigo em Revista Científica Internacional
• Data: 2023

Autores

Julio Rebelo (Autor) Outra; Helena Reis (Autor) FEP

Revista

Título: Moscow Mathematical Journal

Vol. 23 Nº 4

Páginas: 591-624

ISSN: 1609-3321

Editora: Independent University of Moscow

Indexação

ISI Web of Knowledge - 0 Citações

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Outras Informações

ID Authenticus: P-00Z-FG7

DOI: 10.17323/1609-4514-2023-23-4-591-624

Abstract (EN): Let F be a one-dimensional holomorphic foliation defined on a complex projective manifold and consider a meromorphic vector field X tangent to F. In this paper, we prove that if the set of integral curves of X that are given by meromorphic maps defined on C is large enough, then the restriction of F to any invariant complex 2-dimensional analytic set admits a first integral of Liouvillean type. In particular, on C-3, every rational vector field whose solutions are meromorphic functions defined on C admits an invariant analytic set of dimension 2 such that the restriction of the vector field to it yields a Liouville integrable foliation.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 34